Generalized Oscillatory Integrals and Fourier Integral Operators
偏微分方程分析
2007-05-23 v1
摘要
In this article, a theory of generalized oscillatory integrals (OIs) is developed whose phase functions as well as amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distribution data. The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets.
引用
@article{arxiv.math/0607706,
title = {Generalized Oscillatory Integrals and Fourier Integral Operators},
author = {Claudia Garetto and Guenther Hoermann and Michael Oberguggenberger},
journal= {arXiv preprint arXiv:math/0607706},
year = {2007}
}